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Scope and Sequence
2009-2010
TEXARKANA INDEPENDENT SCHOOL DISTRICT
I = Introduced P = Practiced M= Mastered
111.23 Mathematics, Grading Period
Grade 7. Middle School 1 2 3 4 5 6
(1) The student represents and uses numbers in a variety of
equivalent forms. The student is expected to:
(A) compare and order integers and positive rational numbers
•Using multiple forms of positive rational numbers, including
I P P P M
numbers represented as fractions, percents, decimals, positive
and negative integers within a single problem.
(B) convert between fractions, decimals, whole numbers, and
percents mentally, on paper, or with a calculator I P P P M
Including mixed numbers
(C) represent squares and square roots using geometric models I P P M
(2) The student adds, subtracts, multiplies, or divides to solve
problems and justify solutions. The student is expected to:
(A) represent multiplication and division situations involving
fractions and decimals with models, including concrete objects,
I P P P M
pictures, words, and numbers
Including writing or selecting the correct expression
(B) use addition, subtraction, multiplication, and division to solve
problems involving fractions and decimals
I P P P M
Examples include:
Problems where your answer choices are models
(C) use models, such as concrete objects, pictorial models, and
number lines, to add, subtract, multiply, and divide integers and I P P P M
connect the actions to algorithms
(D) use division to find unit rates and ratios in proportional
relationships such as speed, density, price, recipes, and student-
teacher ratio
I P P M
Including:
•Fractions and decimals
•Cross multiply and solve for x
(E) simplify numerical expressions involving order of operations
and exponents I P P P M
Including negative values
(F) select and use appropriate operations to solve problems and
justify the selections
Examples include: IP P P P M
•Problems with multiple operations
•Problems with answer grids
(G) determine the reasonableness of a solution to a problem
Including problems with the appropriate range IP P P P M
(3) The student solves problems involving direct proportional
relationships. The student is expected to:
(A) estimate and find solutions to application problems involving
percent
Including:
I P M
•Percent increase
•Percent decrease
(B) estimate and find solutions to application problems involving
proportional relationships such as similarity, scaling, unit costs,
and related measurement units
Including:
I P P M
•Setting up a proportion problem from word problems
•Using data in a table
•Measurements using standard and metric units
•Unit conversions
(4) The student represents a relationship in numerical,
geometric, verbal, and symbolic form. The student is
expected to:
(A) generate formulas involving unit conversions, perimeter, area,
circumference, volume, and scaling
Including:
•Perimeter of regular polygons
•Circumference
•Area of squares, rectangles, triangles, circles, trapezoids
IP PM
•Volume of rectangular prism, cylinders, cubes
•Conversion from one standard unit to another as listed on the
formula chart
•Conversion from one metric unit to another as listed on the
formula chart
(B) graph data to demonstrate relationships in familiar concepts
such as conversions, perimeter, area, circumference, volume,
and scaling
Including:
•Vocabulary (i.e. independent and dependent variable)
•Data that models a linear relationship. Example: Perimeter IP M
and conversions
•Data that models a quadratic (second degree) relationship.
Example: Area
•Data that models a third degree relationship.
Example: Volume
(C) use words and symbols to describe the relationship between the
terms in an arithmetic sequence (with a constant rate of change)
and their positions in the sequence
Including: I P P M
•The nth term table
•Finding the nth term
•Using nth term to find a specific term
(5) The student uses equations to solve problems. The student is
expected to:
(A) use concrete and pictorial models to solve equations and use
symbols to record the actions I P P P M
Including equations with two variables
(B) formulate problem situations when given a simple equation and
formulate an equation when given a problem situation
Including prerequisites of:
•Translating word phrases to algebraic expressions I P P P M
•Translating word phrases to algebraic equations.
Including focusing on operational vocabulary (Examples:
difference, total, product, and quotient)
(6) The student compares and classifies two- and three-
dimensional figures using geometric vocabulary and
properties. The student is expected to:
(A) use angle measurements to classify pairs of angles as
complementary or supplementary
Including: IP P M
•Diagrams with multiple angles
•Prerequisite: name angles with three points
(B) use properties to classify triangles and quadrilaterals
Including:
•Triangle vocabulary: (i.e. acute, obtuse, right (define legs and
IP PM M
hypotenuse), equiangular, isosceles, equilateral, and scalene)
•Quadrilateral terms: (i.e. parallelogram, rectangle, square,
trapezoid, and rhombus)
(C) use properties to classify three-dimensional figures, including
pyramids, cones, prisms, and cylinders
IP PM
Including vocabulary (i.e. faces, edges, vertices, bases, and
lateral face)
(D) use critical attributes to define similarity
Include:
All polygons
Corresponding sides are proportional
I P P M
Corresponding angles are congruent
Using proportions to find missing sides
Identifying pictorially similar figures
•Students needing to identify corresponding angles and sides by
a similarity statement. Example: ∆ABC similar ~ ∆DEF
(7) The student uses coordinate geometry to describe location
on a plane. The student is expected to:
(A) locate and name points on a coordinate plane using
ordered pairs of integers
Include:
IP P M
•All four quadrants
•Vocabulary: (i.e. x-axis, x-coordinate, y-coordinate, quadrants,
origin)
(B) graph reflections across the horizontal or vertical axis and
graph translations on a coordinate plane
Include all four quadrants I P M
•Reflection across x-axis (x,y) → (x,-y)
•Reflection across y-axis (x,y) → (-x,y)
(8) The student uses geometry to model and describe the
physical world. The student is expected to:
(A) sketch three-dimensional figures when given the top, side, and
IP PM
front views
(B) make a net (two-dimensional model) of the surface area of a
three-dimensional figure
Include figures such as:
•Cylinders
IP PM
•Cones
•Prisms
•Pyramids
•Cube
(C) use geometric concepts and properties to solve problems in
fields such as art and architecture
Include all two- and three-dimensional figures listed on the IP PM
formula chart and combinations of figures such as a half circle
and rectangle pieced together.
(9) The student solves application problems involving
estimation and measurement. The student is expected to:
(A) estimate measurements and solve application problems
involving length (including perimeter and circumference) and
area of polygons and other shapes
Include: IP PM
•All polygons on the formula chart
•Using rulers on formula chart
•Problems with answer grids
(B) connect models for volume of prisms (triangular and
rectangular) and cylinders to formulas of prisms (triangular and
rectangular) and cylinders IP PM
Including matching nets and models to appropriate formulas to
problem solve.
(C) estimate measurements and solve application problems IP PM
involving volume of prisms (rectangular and triangular) and
cylinders
(10) The student recognizes that a physical or mathematical
model can be used to describe the experimental and
theoretical probability of real-life events. The student is
expected to:
(A) construct sample spaces for simple or composite experiments
Including with and without replacement. IPM
Construct tree diagrams
(B) find the probability of independent events
Including:
•Flipping a coin
•Drawing an object from a box without looking IPM
•Compound events: Drawing an object from a box without
looking, replacing the object, and drawing another object
(and/or situations)
(11) The student understands that the way a set of data is
displayed influences its interpretation. The student is
expected to:
(A) select and use an appropriate representation for presenting and
displaying relationships among collected data, including line
plot, line graph, bar graph, stem and leaf plot, circle graph, and
Venn diagrams, and justify the selection I PM
Including:
•Frequency tables
•Vocabulary (i.e. intervals, scale)
(B) make inferences and convincing arguments based on an
analysis of given or collected data I PM
Including using the data to make predictions.
(12) The student uses measures of central tendency and range
to describe a set of data. The student is expected to:
(A) describe a set of data using mean, median, mode, and range P M
(B) choose among mean, median, mode, or range to describe a set
of data and justify the choice for a particular situation
Including problems such as: I PM
Given a set of data the student selects the “best” measure of
central tendency to describe that data
(13) The student applies Grade 7 mathematics to solve problems
connected to everyday experiences, investigations in other
disciplines, and activities in and outside of school. The
student is expected to:
(A) identify and apply mathematics to everyday experiences, to
activities in and outside of school, with other disciplines, and
with other mathematical topics IP P P P PM
This student expectation can be tested in every strand including
one or more than one TEKS at a time.
(B) use a problem-solving model that incorporates understanding
the problem, making a plan, carrying out the plan, and
evaluating the solution for reasonableness IP P P P PM
This student expectation can be tested in every strand including
one or more than one TEKS at a time.
(C) select or develop an appropriate problem-solving strategy from
a variety of different types, including drawing a picture,
looking for a pattern, systematic guessing and checking, acting
it out, making a table, working a simpler problem, or working IP P P P PM
backwards to solve a problem
This student expectation can be tested in every strand including
one or more than one TEKS at a time.
(D) select tools such as real objects, manipulatives, paper/pencil,
and technology or techniques such as mental math, estimation, I P P P PM
and number sense to solve problems
(14) The student communicates about Grade 7 mathematics
through informal and mathematical language,
representations, and models. The student is expected to:
(A) communicate mathematical ideas using language, efficient
tools, appropriate units, and graphical, numerical, physical, or
algebraic mathematical models I P P P PM
This student expectation can be tested in every strand including
one or more than one TEKS at a time.
(B) evaluate the effectiveness of different representations to
I PM
communicate ideas
(15) The student uses logical reasoning to make conjectures and
verify conclusions. The student is expected to:
(A) make conjectures from patterns or sets of examples and non-
examples
Including:
•Defining a concept introduced at a higher grade IP P P M
•Showing a pattern, examples, and/or non-examples
•Expecting students to choose a correct response by analyzing
the pattern, examples, or non-examples
(B) validate his/her conclusions using mathematical properties and
relationships
I P P P M
This student expectation can be tested in every strand including
one or more than one TEKS at a time.
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